Simplify the following expression: $r = \dfrac{p}{3p} - \dfrac{7p - 3}{3p}$
Answer: Since the expressions have the same denominator we simply subtract the numerators: $r = \dfrac{p - (7p - 3)}{3p}$ Distribute the negative sign: $r = \dfrac{p - 7p + 3}{3p}$ Combine like terms: $r = \dfrac{-6p + 3}{3p}$ Simplify by dividing numerator and denominator by 3: $r = \dfrac{-2p + 1}{p}$